This invention relates to determination of differences between ellipsoids associated with different datums in surveying activities.
A survey of locations at a survey site may involve use of location coordinates from previously-surveyed locations (xe2x80x9ccontrol survey pointsxe2x80x9d), such as recognizable landmarks and other survey monuments, together with generation of location coordinates for newly-surveyed locations. Even where location coordinates for only newly-surveyed locations are used, these coordinates may not be fully consistent with each other when corrections are made for any errors introduced by use of a local coordinate system. The location coordinates of these locations, representing newly-surveyed locations and/or previously-surveyed locations, must be made consistent with each other in some xe2x80x9cbest fitxe2x80x9d sense.
Survey of a chosen region often requires use of a globally defined survey ellipsoid, such as the NAD27, NAD83 or WGS84 ellipsoid, and of a locally defined ellipsoid that takes account of the local terrain. A globally defined survey ellipsoid is intended to provide a best fit, in some quantitative sense, to the terrain for the entire Earth. A locally defined ellipsoid, by contrast, is only intended to provide a best fit for a locally defined region and thus may provide a better fit over this limited region.
In a survey of a local region, location coordinates may first be obtained using a first, globally defined datum C1, after which these coordinates are re-expressed in terms of a second datum C2, which may be globally defined or locally defined, using a coordinate transformation T. Accurate coordinates for a plurality of survey control points are often available, and these survey control point coordinates are often used to xe2x80x9canchorxe2x80x9d the transformation of location coordinates for other survey points.
Coordinate differences between a point p(x,y,z) in the first, globally defined datum Cl and the corresponding point pxe2x80x2(xxe2x80x2,yxe2x80x2,zxe2x80x2) in the second datum C2 are presently determined, using a point-by-point approach in which the group of survey control points chosen for xe2x80x9canchoringxe2x80x9d can vary with the local terrain. FIG. 1 illustrates a vector difference xcex94r=(xxe2x80x2-x, yxe2x80x2-y, zxe2x80x2-z) between point coordinates (x,y,z) on a surface S1, defined using the datum C1, and the corresponding point coordinates (xxe2x80x2,yxe2x80x2,zxe2x80x2) on a corresponding surface S2, defined using the datum C2. In the past, these coordinate differences were determined point-by-point on each of a plurality of sub-regions or patches that together make up a survey region SR, and these differences were often not continuous or consistent in moving from one sub-region to a contiguous sub-region. Thus, the coordinate differences had to be recomputed by applying the transformation T to each new point in the first datum; and parameters defining the transformation T might change in moving from one sub-region to a contiguous sub-region.
Several workers have considered the problems of representation of locations on a map or chart display and/or adjustment of location coordinates. Previous workers in this field often assume that the coordinates for locations of interest in a coordinate system, or in two or more associated coordinate systems, are consistent with each other. Further, the computations and coordinate manipulations are usually performed in a post-processing environment, rather than in a real time environment in the field at the time the survey measurements are made.
What is needed is an approach that allows real time processing, or post processing, to determine and apply a survey coordinate transformation between the first datum and the second datum in a chosen region that varies continuously and consistently with the point chosen in the region. Preferably, this transformation should be optimal in some sense over a grid of survey control points, and the transformation should depend only minimally or not at all on the particular grid chosen for such optimization. Preferably, this approach should allow use of any of a variety of generally defined coordinate transformations, each with its own set of transformation parameters that are to be optimized based on the survey control constraints imposed.
These needs are met by the invention, which provides a system for determination and application of a transformation, between a first, globally defined datum and a second datum over a chosen region, that varies continuously with the (arbitrary) choice of survey points within the region. A region is chosen, and a finite number N of survey control points is identified within the region. In most situations, Nxe2x89xa73 is preferred, but in certain situations N=2 survey control points will suffice. A two-dimensional grid is defined over the region; and for each point p=PG on the grid a transformation T, from first datum to second datum and having one or more adjustable parameters, is determined that is optimal, in the sense that the coordinate difference between first datum and second datum is xe2x80x9cas close as possiblexe2x80x9d to the accurately known difference for each of K survey control points that are xe2x80x9cclosest toxe2x80x9d the chosen grid point, where Kxe2x89xa6N. Each chosen grid point PG may have a different optimal transformation T associated with the grid point.
Three coordinate differences (one for each of latitude, longitude and height), computed using the transformation T at the chosen grid point PG, are associated with each grid point, thus forming three grids of difference values. For these three grids of difference values, a continuously variable interpolation function is determined that (1) substantially matches coordinate difference values at each grid point, either exactly or as closely as possible in some least qth power sense, and (2) extends each difference value grid to survey points that are not part of the original grid of points.
The transformation T between the first datum and the second datum may be one of the well-known four-parameter, six-parameter, seven-parameter or 12-parameter transformations used in survey work, as discussed in U.S. Pat. No. 5,614,913, issued to Nichols et al and incorporated by reference herein. Alternatively, the transformation T may be any other suitable adjustable parameter transformation between the two datums.
All these determinations of transformations and interpolation mappings between corresponding survey locations can be made in the field in near-real time, or these determinations can be made by post-processing after the survey crew returns to the office. The invention will be most useful for in-the-field determinations, where errors in measurement, or in assumptions concerning a local coordinate system used for such measurements, can be promptly corrected if necessary.